H∞ fuzzy output feedback control design for nonlinear systems: an LMI approach

This paper addresses the problem of stabilising a class of nonlinear systems by using an H_∞ fuzzy output feedback controller. First, a nonlinear system is approximated by a Takagi-Sugeno fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an H_∞ fuzzy output feedback control law which globally stabilises this class of nonlinear systems. A design algorithm for constructing a stabilising H_∞ fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the H_∞ fuzzy output feedback controller are allowed to be different from the premise variables of the Takagi-Sugeno fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development